How many words can be formed by taking two identical and two distinct letters from the letters of the word $COMBINATION$?

Let the eleven letters $A, B, ....., K$ denote an arbitrary permutation of the integers $(1, 2, ....., 11)$. Then,what is the nature of the product $(A - 1)(B - 2)(C - 3) ..... (K - 11)$?

Numbers are to be formed between $1000$ and $3000$,which are divisible by $4$,using the digits $1, 2, 3, 4, 5$ and $6$ without repetition of digits. Then the total number of such numbers is.

The number of $9$-digit even natural numbers formed using only the digits $0$ and $1$,such that no two consecutive digits are $0$,is:

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways,in which a team of $3$ students can be randomly selected from this group such that there is at least one boy and at least one girl in each team,is $1750$,then $n$ is equal to

Five boys and five girls are writing an examination in a hall in which $5$ benches are arranged in a row and only two students are to be seated on every bench at either of its ends. If the seating arrangement is to be such that no two boys or no two girls sit together as neighbours (a student should not have a student of same gender either on left or right),then the total number of such arrangements is